Britain's vote to leave the European Union has left the country's universities with a problem to solve -- how to plug a funding gap and maintain prestige if the flood of students from across the EU slows to a trickle.

Before the June 23 referendum backed a British exit, or Brexit, the heads of about 80 percent of British universities issued a joint appeal to "Remain" in the 28-country bloc.

Since the vote, universities have been trying to calm their overseas students and to reassure applicants from abroad that nothing will change -- at least for now because the process of leaving the EU is expected to take at least two years.

In the longer term, they fear their funding, attractiveness to foreign students and academic prestige will decline.

"I cherish European values," said Bettina Sakiotis, a 17-year-old Greek living in Luxembourg who has been offered a place by two English universities from October. "Voting for Brexit shows ... we are not on the same page."

After the referendum, she considered taking a place instead at Italy's Bocconi University in Milan. In the end, she decided on Britain but she still has doubts.

"I think (Brexit) will have serious political consequences for the UK," she said. "I feel the UK is isolating itself."

Universities in Britain do not know yet whether the outcome of the referendum will affect international student admissions for the coming academic year. Places will largely be allocated in August, when this year's school exam results come through.

But much is at stake for some universities. One in three people studying for a first degree at the universities of Essex and Kent, for example, are international students, according to The Complete University Guide, a publisher of university league tables.

There are 125,000 students from the EU in higher education in Britain, about 5.5 percent of the total, and the proportion is much higher at some universities -- rising to about 16 percent at Cambridge, for example.

The battle has begun to hang on to those already planning to come to a country that hosts three of the world's top 10 universities -- Oxford, Cambridge and Imperial College London, according to The Times Higher Education World University rankings. Six of the other seven are in the United States.

EU students currently pay the same fees as British students but many fear the cost of attending a British university will soar if they are treated as overseas students after a British exit from the EU.

"There will be no changes to the immigration or fee status of EU students entering Newcastle University in 2016 entry," Chris Brink, vice-chancellor of Newcastle University, wrote on the university's website. "You will pay the UK rate of fee for the full duration of your programme of study."

The university later extended this promise to the 2017 intake, but like other institutions further commitments were uncertain as the details of Brexit remain up in the air.

Questions over funding

Higher education was not a big issue outside academia during campaigning for the referendum, but the Leave campaign said that money saved from leaving the EU could be channelled into whatever Britain wants, including science research.

It is not just students' fees that could be affected.

Universities UK, which represents university heads, says their institutions received more than 836 million pounds ($1.11 billion) in research grants and contracts from EU sources in 2014-15.

Such research funding generates more than 19,000 jobs across Britain and translates into 1.86 billion pounds for the British economy, it said.

"More than 60 percent of the UK's international research partners are from other EU countries," Universities UK said in a statement. "This is growing faster than any of our other collaborative research relationships."

Among the areas of concern are Britain's participation in the Erasmus+ programme which funds exchanges of students and teachers across EU higher education institutions.

More than 27,000 EU students came to study or train in Britain with an Erasmus grant in 2013-14 as well as more than 3,500 staff.

While Erasmus has a number of non-EU members, Switzerland was effectively suspended when it voted to limit the free movement of people from the EU, an important issue in Britain's exit from the bloc.

British universities are also looking at a status change among a large proportion of their students.

University admissions service UCAS said that for the coming undergraduate year, the number of British applicants declined by 0.3 percent, reflecting demographics, while those from EU countries rose 6 percent.

Undergraduate fees for British and EU students are a maximum of 9,000 pounds a year. They can be much higher for non-EU international students, depending on the university and the course.

At the University of Kent, international students pay up to 15,900 pounds a year. Studying medicine at Imperial College London will set them back 37,100 pounds a year.

Testaments on Facebook

Such a shift could be devastating for British universities if the cost overcame the attractiveness of the study. Michael Arthur, president of University College London, has estimated it could put about 40 million pounds of tuition fee income at risk.

While some of Britain's most celebrated centres of learning may be able to battle through any trouble from Brexit on their reputations, they are not immune to the fears over funding, faculty and appeal.

The influential London School of Economics, which has an overall 18 percent EU student contingent, has urged alumni to post testaments on Facebook to trumpet the institution's EU diversity.

EU students generated 3.7 billion pounds for the British economy in 2011-12 and supported more than 34,000 jobs, according to Universities UK.

Independent fact-checking charity Full Fact estimates British higher education providers get at least 2.6 percent of their total income from the EU, or around 16 percent of their research income.

"The impact of our universities on our local communities and economy should not be underestimated," university vice-chancellors wrote in their joint appeal for Britain to remain in the EU.

The government has not managed so far to give much succour to the institutions or potential students like Sakiotis.

"There are obviously big discussions to be had with our European partners, and I look forward to working with the sector to ensure its voice is fully represented and that it continues to go from strength to strength," Jo Johnson, Britain's university minister, said in a statement.

Universities in the EU are unlikely to wait to take advantage of the uncertainty in British academia. Italian Prime Minister Matteo Renzi has already proposed the EU grant citizenship to British students enrolled in EU countries.